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ARCHIVE / INDEPENDENT MANUSCRIPTS / 2026

THE WORK.
THE REASONING.

Selected independent technical work in mathematical modeling, geometric control, topology, and electromagnetism. Each entry separates analysis and conceptual research from physical validation.

Geometric Control, Actuator Feasibility, and Algebraic Equilibria in a Four-Wheel X-Drive Robot

An analytical study of how a four-wheel X-drive robot can be controlled while respecting the geometry of motion and the constraints imposed by individual wheel actuators.

FORMAT // INDEPENDENT TECHNICAL MANUSCRIPTTOOLS / CONCEPTS // SE(2), KINEMATICS, LIE GROUPSEVIDENCE // ANALYSIS & NUMERICAL CASES

The problem

Omnidirectional robot motion is easy to describe with idealized velocities. The interesting part begins when each wheel has a finite speed range, sensing is imperfect, and the vehicle needs to converge to a desired pose.

My contribution

  • Derived a wheel-speed map and characterized actuator-feasible chassis velocities for a symmetric X-drive.
  • Used wheel effort to motivate a Riemannian metric on chassis motion.
  • Formulated logarithmic pose-error feedback using the geometry of SE(2).
  • Explored algebraic equilibrium structure and numerical motion cases.
Validation boundary: The results describe an idealized analytical framework. Calibration, wheel slip, sensor error, controller implementation, and physical robot experiments remain unresolved. This should not be read as a claim of tested closed-loop performance.
Request manuscript / discuss the model ↗

Persistent Homology and Stochastic Dynamics: Stability in Financial Modeling

A mathematical exploration of whether changes in relational structure, summarized through persistent homology, can be introduced as inputs to stochastic models without sacrificing analytical clarity.

FORMAT // INDEPENDENT RESEARCH MANUSCRIPTTOOLS / CONCEPTS // PERSISTENCE, STOCHASTIC DYNAMICSEVIDENCE // ANALYTICAL EXAMPLES

The question

Cross-asset correlation matrices change over time. Persistent-homology summaries provide one way to study structural differences across such data. Could those summaries become mathematically tractable signals in a stochastic model?

My contribution

  • Defined a modeling direction using lagged topological features of correlation structure.
  • Investigated how perturbations in persistence summaries affect modeled dynamics.
  • Developed stability estimates and an analytical four-asset example.
  • Outlined empirical tests and negative controls needed to evaluate usefulness.
Validation boundary: Stability of a mathematical construction does not establish predictive power or a trading advantage. The forecasting hypothesis has not been empirically validated.
Request manuscript / discuss the mathematics ↗

Topology in Electromagnetic Confinement: Literature Review and Conceptual Synthesis

An independent exploration of how topological reasoning can illuminate questions involving field configurations, electromagnetic confinement, and mathematical descriptions of physical systems.

FORMAT // LITERATURE REVIEWTOOLS / CONCEPTS // TOPOLOGY, FIELD GEOMETRYEVIDENCE // CONCEPTUAL SYNTHESIS

The motivation

Electromagnetic systems are governed by local field equations, but the global organization of those fields also matters. Topology offers a complementary language for asking structural questions.

The work

  • Studied existing research at the intersection of electromagnetic confinement and topology.
  • Connected mathematical concepts to physical interpretations in a literature-based synthesis.
  • Identified directions for deeper theoretical and eventually experimental inquiry.
Validation boundary: This work synthesizes published ideas. It does not report an independently demonstrated confinement device, a novel experimental result, or verified performance gains.
Request review / continue the conversation ↗

MATHEMATICAL RIGOR
IS NOT A PERFORMANCE CLAIM.

My published descriptions distinguish theoretical results, conceptual work and empirical hypotheses. None of these manuscripts alone demonstrates a physically validated controller, a trading advantage or an electromagnetic confinement device. For manuscript inquiries, send an email. For a small hands-on demonstration of the ideas, visit the interactive lab.